To find out how many cans are already on the shelf, we can use the information given to create an equation.
Let \( x \) be the number of cans already on the shelf.
According to the problem, the shelf can hold a total of 58 cans, and Alexei can still put 39 more cans on the shelf. This means the number of cans already on the shelf plus the number of cans that can still be added equals the total capacity of the shelf.
We can set up the equation as follows:
\[ x + 39 = 58 \]
Now we can solve for \( x \):
- Subtract 39 from both sides:
\[ x = 58 - 39 \]
- Calculate the right side:
\[ x = 19 \]
Thus, the number of cans already on the shelf is \( \boxed{19} \).